Question

3) Resolva as equações de 2º grau: a) 4x 2 - 4x + 1 = 0 b) x 2 - 49 = 0 c) x 2 + 9x + 14 = 0 d) x 2 + 3x = 0 e) x 2 – 4x – 5 = 0

Answer 1

a) 4x2 - 4x + 1 = 0

delta = b2 - 4ac

delta = (-4)2 - 4.4.1 = 16 - 16 = 0

x = ( - b +- Vdelta ) / 2.a

x = ( -(-4) +- V0 ) / 2.4 = ( 4 +- 0 ) / 8 = 4 / 8 = 0,5

b) x2 - 49 = 0

x2 = 49

Vx = V49

x = 7

c) x2 + 9x + 14 = 0

delta = 9^2 - 4.1.14 = 81 - 56 = 25

x = ( - 9 +- V25 ) / 2.1 = ( - 9 +- 5 ) / 2

x' = ( - 9 - 5 ) / 2 = - 14 / 2 = - 7

x" = ( - 9 + 5 ) / 2 = - 4 / 2 = - 2

d) x2 + 3x = 0

delta = 3^2 - 4.1.0 = 9 - 0 = 9

x = ( -3 +- V9 ) / 2.1 = ( -3 +- 3 ) / 2

x' = ( - 3 - 3 ) / 2 = - 6 / 2 = - 3

x" = ( - 3 + 3 ) / 2 = 0 / 2 = 0

e) x2 - 4x - 5 = 0

delta = (-4)2 - 4.1.(-5) = 16 + 20 = 36

x = ( -(-4) +- V36 ) / 2.1 = ( 4 +- 6 ) / 2

x' = ( 4 - 6 ) / 2 = - 2 / 2 = - 1

x" = ( 4 + 6 ) / 2 = 10 / 2 =5